daeFunction

Convert system of differential algebraic equations to MATLAB function handle suitable for ode15i

Syntax

f = daeFunction(eqs,vars)

f = daeFunction(eqs,vars,p1,...,pN)

f = daeFunction(___,Name,Value)

Description

f = daeFunction(eqs,vars) converts a system of symbolic first-order differential algebraic equations (DAEs) to a MATLAB^® function handle acceptable as an input argument to the numerical MATLAB DAE solver ode15i.

f = daeFunction(eqs,vars,p1,...,pN) lets you specify the symbolic parameters of the system as p1,...,pN.

f = daeFunction(___,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

Examples

Convert DAE System to Function Handle

Create the system of differential algebraic equations. Here, the symbolic functions x1(t) and x2(t) represent the state variables of the system. The system also contains constant symbolic parameters a, b, and the parameter function r(t). These parameters do not represent state variables. Specify the equations and state variables as two symbolic vectors: equations as a vector of symbolic equations, and variables as a vector of symbolic function calls.

syms x1(t) x2(t) a b r(t)
eqs = [diff(x1(t),t) == a*x1(t) + b*x2(t)^2,...
       x1(t)^2 + x2(t)^2 == r(t)^2];
vars = [x1(t), x2(t)];

Use daeFunction to generate a MATLAB function handle f depending on the variables x1(t), x2(t) and on the parameters a, b, r(t).

f = daeFunction(eqs, vars, a, b, r(t))

f = 
  function_handle with value:
    @(t,in2,in3,param1,param2,param3)[in3(1,:)-param1.*in2(1,:)...
-param2.*in2(2,:).^2;-param3.^2+in2(1,:).^2+in2(2,:).^2]

Specify the parameter values, and create the reduced function handle F as follows.

a = -0.6;
b = -0.1;
r = @(t) cos(t)/(1 + t^2);
F = @(t, Y, YP) f(t,Y,YP,a,b,r(t));

Specify consistent initial conditions for the DAE system.

t0 = 0;
y0 = [-r(t0)*sin(0.1); r(t0)*cos(0.1)];
yp0= [a*y0(1) + b*y0(2)^2; 1.234];

Now, use ode15i to solve the system of equations.

ode15i(F, [t0, 1], y0, yp0)

Write Function to File with Comments

Write the generated function handle to a file by specifying the File option. When writing to a file, daeFunction optimizes the code using intermediate variables named t0, t1, .… Include comments in the file using the Comments option.

Write the generated function handle to the file myfile.

syms x1(t) x2(t) a b r(t)
eqs = [diff(x1(t),t) == a*x1(t) + b*x2(t)^2,...
       x1(t)^2 + x2(t)^2 == r(t)^2];
vars = [x1(t), x2(t)];
daeFunction(eqs, vars, a, b, r(t), 'File', 'myfile')

function eqs = myfile(t,in2,in3,param1,param2,param3)
%MYFILE
%    EQS = MYFILE(T,IN2,IN3,PARAM1,PARAM2,PARAM3)

%    This function was generated by the Symbolic Math Toolbox version 7.3.
%    01-Jan-2017 00:00:00

YP1 = in3(1,:);
x1 = in2(1,:);
x2 = in2(2,:);
t2 = x2.^2;
eqs = [YP1-param2.*t2-param1.*x1;t2-param3.^2+x1.^2];

Include the comment Version: 1.1.

daeFunction(eqs, vars, a, b, r(t), 'File', 'myfile',...
                    'Comments','Version: 1.1');

function eqs = myfile(t,in2,in3,param4,param5,param6)
...
%Version: 1.1
YP3 = in3(1,:);
...

Input Arguments

eqs — System of first-order DAEs

vector of symbolic equations | vector of symbolic expressions

System of first-order DAEs, specified as a vector of symbolic equations or expressions. Here, expressions represent equations with zero right side.

vars — State variables

vector of symbolic functions | vector of symbolic function calls

State variables, specified as a vector of symbolic functions or function calls, such as x(t).

Example: [x(t),y(t)] or [x(t);y(t)]

p1,...,pN — Parameters of system

symbolic variables | symbolic functions | symbolic function calls | symbolic vector | symbolic matrix

Parameters of the system, specified as symbolic variables, functions, or function calls, such as f(t). You can also specify parameters of the system as a vector or matrix of symbolic variables, functions, or function calls. If eqs contains symbolic parameters other than the variables specified in vars, you must specify these additional parameters as p1,...,pN.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: daeFunction(eqns,vars,'File','myfile')

'Comments' — Comments to include in file header

character vector | cell array of character vectors | string vector

Comments to include in the file header, specified as a character vector, cell array of character vectors, or string vector.

'File' — Path to file containing generated code

character vector

Path to the file containing generated code, specified as a character vector. The generated file accepts arguments of type double, and can be used without Symbolic Math Toolbox™. If the value is an empty character vector, odeFunction generates an anonymous function. If the character vector does not end in .m, the function appends .m.

By default, daeFunction with the File argument generates a file containing optimized code. Optimized means intermediate variables are automatically generated to simplify or speed up the code. MATLAB generates intermediate variables as a lowercase letter t followed by an automatically generated number, for example t32. To disable code optimization, use the Optimize argument.

'Optimize' — Flag preventing optimization of code written to function file

true (default) | false

Flag preventing optimization of code written to a function file, specified as false or true.

By default, daeFunction with the File argument generates a file containing optimized code. Optimized means intermediate variables are automatically generated to simplify or speed up the code. MATLAB generates intermediate variables as a lowercase letter t followed by an automatically generated number, for example t32.

daeFunction without the File argument (or with a file path specified by an empty character vector) creates a function handle. In this case, the code is not optimized. If you try to enforce code optimization by setting Optimize to true, then daeFunction throws an error.

'Sparse' — Flag that switches between sparse and dense matrix generation

false (default) | true

Flag that switches between sparse and dense matrix generation, specified as true or false. When you specify 'Sparse',true, the generated function represents symbolic matrices by sparse numeric matrices. Use 'Sparse',true when you convert symbolic matrices containing many zero elements. Often, operations on sparse matrices are more efficient than the same operations on dense matrices.

Output Arguments

f — Function handle that can serve as input argument to ode15i

MATLAB function handle

Function handle that can serve as input argument to ode15i, returned as a MATLAB function handle.